AROMAN: Alternative Ranking Order Method Accounting for Two-Step Normalisation

Overview

Two-step normalisation (linear + vector) with weighted power aggregation. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Two-step normalisation (linear + vector) with weighted power aggregation

Limitations

• •Assumes: Criteria preferences are independent (no synergistic interactions)
• •Assumes: Compensation is acceptable: high score on one criterion can offset low on another
• •Assumes: Decision matrix is complete (no missing values)

Assumptions to verify

• •Criteria preferences are independent (no synergistic interactions)
• •Compensation is acceptable: high score on one criterion can offset low on another
• •Decision matrix is complete (no missing values)

When not to use

• •Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• •Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Edge cases

• •default (paper Eq. 8). Note: normalization in Steps 1-2 has NO direction inversion; L_i (cost sum) and A_i (benefit sum) are raw minmax/vector values. Bošković et al. 2023, IEEE Access DOI:10.1109/ACC

Common pitfalls

• •Hatalı: 'AROMAN bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'AROMAN bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'AROMAN bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: AROMAN'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: AROMAN'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Dual normalisation: linear (T¹) + vector (T²). Formül: T^{1}_{ij}=\dfrac{x_{ij}-\min_{i} x_{ij}}{\max_{i} x_{ij}-\min_{i} x_{ij}};\quad T^{2}_{ij}=\dfrac{x_{ij}}{\sqrt{\sum_{k} x_{kj}^{2}}} Anchor: Bošković 2023, p.4 Eqs.(1)-(2)
2. 2.Adım 2 (F2): Step 2: Combined normalisation Z_ij = (β T¹_ij + (1−β) T²_ij)/2 with β ∈ [0,1]. Formül: Z_{ij} = \dfrac{\beta T^{1}_{ij} + (1-\beta) T^{2}_{ij}}{2} Anchor: Bošković 2023, p.4 Eq.(3)
3. 3.Adım 3 (F3): Step 3: Weighted matrix v_ij = w_j Z_ij. Formül: v_{ij} = w_{j}\,Z_{ij} Anchor: Bošković 2023, p.5 Eq.(4)
4. 4.Adım 4 (F4): Step 4: Sum of benefit Σ^+_i and cost Σ^−_i criteria. Formül: \Sigma^{+}_{i}=\sum_{j\in J^{+}} v_{ij},\quad \Sigma^{-}_{i}=\sum_{j\in J^{-}} v_{ij} Anchor: Bošković 2023, p.5 Eqs.(5)-(6)
5. 5.Adım 5 (F5): Step 5: AROMAN score R_i = (Σ^−_i)^λ + (Σ^+_i)^(1−λ) and descending ranking. λ=0.5 default (paper Eq. 8). Note: normalization in Steps 1-2 has NO direction inversion; L_i (cost sum) and A_i (benefit sum) are raw minmax/vector values. Bošković et al. 2023, IEEE Access DOI:10.1109/ACCESS.2023.3265818. Formül: R_{i} = (\Sigma^{-}_{i})^{\lambda} + (\Sigma^{+}_{i})^{1-\lambda},\ \lambda\in[0,1],\ \text{rank descending} Anchor: Bošković 2023, p.6 Eq.(7)

Commonly paired with

• •AHP + AROMAN (high)
• •BWM + AROMAN (high)
• •ENTROPY + AROMAN (high)
• •CRITIC + AROMAN (high)
• •SWARA + AROMAN (high)

How to cite